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Front. Inform. Technol. Electron. Eng.  2012, Vol. 13 Issue (12): 901-908    DOI: 10.1631/jzus.C1200180
    
Learning robust principal components from L1-norm maximization
Ding-cheng Feng, Feng Chen, Wen-li Xu
Tsinghua National Laboratory for Information Science and Technology, Tsinghua University, Beijing 100084, China; Department of Automation, Tsinghua University, Beijing 100084, China
Learning robust principal components from L1-norm maximization
Ding-cheng Feng, Feng Chen, Wen-li Xu
Tsinghua National Laboratory for Information Science and Technology, Tsinghua University, Beijing 100084, China; Department of Automation, Tsinghua University, Beijing 100084, China
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摘要： Principal component analysis (PCA) is fundamental in many pattern recognition applications. Much research has been performed to minimize the reconstruction error in L1-norm based reconstruction error minimization (L1-PCA-REM) since conventional L2-norm based PCA (L2-PCA) is sensitive to outliers. Recently, the variance maximization formulation of PCA with L1-norm (L1-PCA-VM) has been proposed, where new greedy and non-greedy solutions are developed. Armed with the gradient ascent perspective for optimization, we show that the L1-PCA-VM formulation is problematic in learning principal components and that only a greedy solution can achieve robustness motivation, which are verified by experiments on synthetic and real-world datasets.
关键词： Principal component analysis (PCA);  Outliers;  L1-norm;  Greedy algorithms;  Non-greedy algorithms    
Abstract: Principal component analysis (PCA) is fundamental in many pattern recognition applications. Much research has been performed to minimize the reconstruction error in L1-norm based reconstruction error minimization (L1-PCA-REM) since conventional L2-norm based PCA (L2-PCA) is sensitive to outliers. Recently, the variance maximization formulation of PCA with L1-norm (L1-PCA-VM) has been proposed, where new greedy and non-greedy solutions are developed. Armed with the gradient ascent perspective for optimization, we show that the L1-PCA-VM formulation is problematic in learning principal components and that only a greedy solution can achieve robustness motivation, which are verified by experiments on synthetic and real-world datasets.
Key words: Principal component analysis (PCA)    Outliers    L1-norm    Greedy algorithms    Non-greedy algorithms
收稿日期: 2012-06-11 出版日期: 2012-12-09
CLC:  TP391.4  
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Ding-cheng Feng
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Ding-cheng Feng, Feng Chen, Wen-li Xu. Learning robust principal components from L1-norm maximization. Front. Inform. Technol. Electron. Eng., 2012, 13(12): 901-908.

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http://www.zjujournals.com/xueshu/fitee/CN/10.1631/jzus.C1200180    或    http://www.zjujournals.com/xueshu/fitee/CN/Y2012/V13/I12/901

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